Each year U.S. News and World Report conducts its "Survey of America's Best Graduate and Professional Schools." and ranks the top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate. For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. An academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. The results of a simple linear regression of SALARY versus GMAT using the 25 data points are shown below. Is there sufficient evidence to suggest there is a linear relationship between SALARY and GMAT at the 5% level of significance? ----------------------------------------------------------------------------------- a = -92040 b = 228 s = 3213 r2 = .66 r = .81 df = 23 t = 6.67 (the test statistic) a) There is enough evidence (at α = .05) to suggest that there is a linear relationship between SALARY and GMAT. b) Only 6.67% of the sample variation in SALARY can be explained by using GMAT in a straight-line model. c) There is not enough evidence (at α = .05) of at least a positive linear relationship between SALARY and GMAT. d) We estimate SALARY to increase $6.67 for every 1-point increase in GMAT.
Each year U.S. News and World Report conducts its "Survey of America's Best Graduate and Professional Schools." and ranks the top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student.
An academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. The results of a simple linear regression of SALARY versus GMAT using the 25 data points are shown below. Is there sufficient evidence to suggest there is a linear relationship between SALARY and GMAT at the 5% level of significance? -----------------------------------------------------------------------------------
a = -92040 b = 228 s = 3213 r2 = .66 r = .81 df = 23 t = 6.67 (the test statistic)
a) There is enough evidence (at α = .05) to suggest that there is a linear relationship between SALARY and GMAT.
b) Only 6.67% of the sample variation in SALARY can be explained by using GMAT in a straight-line model.
c) There is not enough evidence (at α = .05) of at least a positive linear relationship between SALARY and GMAT.
d) We estimate SALARY to increase $6.67 for every 1-point increase in GMAT.
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